A river is flowing with velocity `5km//hr` as shown in the figure. A boat start from A and reaches the other bank by covering shortest possible distance. Velocity of boat in still water is `3km//hr`. The distance boat covers is.

Options

A. `500 m`
B. `400 sqrt(2)m`
C. `300 sqrt(2) m`
D. `600 m`

Answer

A

Explanation

When `v_(r) gt v_(br)`
`{:("for minimum drift",,v_(r)=5 km//hr),(,,v_(br)=3 km//hr),(sin theta=v_(br)/v_(r)=3/5,,b=300 m=0.3 km):}`
`theta=37^(@)`
velocity of boat along x-axis
so `v_(x)=v_(r)-v_(br) sin theta`
`v_(x)=5/1-3xx3/5=16/5 km//hr`
velocity of boat along y-axis
`v_(y)=v_(br) cos theta=3xx4/5=12/5 km//hr`
Time of crossing `T=b/v_(y)=(0.3xx5)/12xx1/10=1/8` hrs.
Drift `x=v_(x)xxT=16/5xx1/8=0.4 km=400 m`
So distance travelled by boat
`S=sqrt(b^(2)+x^(2))=500 m`